Let be a particular value of . Find the value of such that

Chapter 7, Problem 82E

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QUESTION:

Let \(X_{0}^{2}\) be a particular value of \(X^2\). Find the value of \(X_{0}^{2}\) such that

a. \(P\left(x^{2}\ >\ x_{0}^{2}\right)=.10 \text { for } n=12\)

b. \(P\left(x^{2}\ >\ x_{0}^{2}\right)=.05 \text { for } n=9\)

c. \(P\left(x^{2}\ >\ x_{0}^{2}\right)=.025 \text { for } n=5\)

Questions & Answers

QUESTION:

Let \(X_{0}^{2}\) be a particular value of \(X^2\). Find the value of \(X_{0}^{2}\) such that

a. \(P\left(x^{2}\ >\ x_{0}^{2}\right)=.10 \text { for } n=12\)

b. \(P\left(x^{2}\ >\ x_{0}^{2}\right)=.05 \text { for } n=9\)

c. \(P\left(x^{2}\ >\ x_{0}^{2}\right)=.025 \text { for } n=5\)

ANSWER:

Solution:

Step 1 of 3:

Let  be the particular value of

  1. We have  P(> ) = 0.10 for n = 12

The claim is to find the value of  

We have n = 12 and df = n - 1

                                       = 12 - 1

                                        = 11

We have to check for 11th row and 0.10 column in chi-square table

   Therefore,  = 17.275.


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